X-ray transmission imaging systems, such as projection imaging, tomosynthesis, and computed tomography (CT), create images of materials based on their density and energy-dependent x-ray attenuation properties. Typical x-ray imaging systems use an x-ray beam with a polyenergetic x-ray spectrum. However, conventional x-ray imaging systems do not collect information about the energy content of the detected signal across multiple spectra, meaning that information about the material-specific energy-dependent signature of an image object is lost. Because of this lost information, materials with different compositions may be indistinguishable in the resulting x-ray image. For example, two different types of kidney stones may look the same on a regular CT scan despite the fact that the kidney stones are comprised of different materials. In another example, iodine (which is injected to provide contrast to the blood) can sometimes be indistinguishable in a regular CT scan to a calcified plaque in a blood vessel despite the fact that the iodine and the calcified plaque have different compositions.
New imaging techniques are being developed to collect multi-spectral data, which can be utilized to determine information about material composition of an imaged object. One currently-available method of processing measured multi-spectral x-ray data to extract information about material composition of an object is to decompose the multi-spectral data into basis functions, resulting in a set of basis coefficients for each measurement. A mathematical relationship between the basis coefficients and the multi-spectral x-ray data is known for the case of ideal systems and can be solved numerically using existing algorithms. This method is complicated by the fact that, in practice, the x-ray imaging process is affected by physical nonidealities that make it difficult to solve for the basis coefficients with existing methods. Material decomposition can be performed by solving a set of linear equations for mono-energetic x-ray transmissions assuming perfect detectors.
The problem becomes even more difficult and nonlinear when using a standard x-ray beam consisting of varying energy photons and when considering the effects of the non-ideal detector. Existing technologies for material decomposition from multi-spectral x-ray data include compensatory algorithms for non-ideal detector responses based on the laws governing physical processes. Models of the detector's energy response and pulse pileup must be used. These models are parameterized based on the specific brand and type of the detector and may require radioactive isotopes for determining the parameters. The gold standard is the maximum likelihood estimator, which is iterative in nature and performs poorly without prior knowledge of system parameters. In addition, empirical methods exist using calibration data to create correction look-up tables. These algorithms may require significant processing power or computer memory, require prior knowledge of the system, and may not sufficiently model the underlying phenomena entirely, leading to less accurate results.